Abstract
Letf(d)f(d)be the smallest number so that every set inRd{R^d}of diameter 1 can be partitioned intof(d)f(d)sets of diameter smaller than 1. Borsuk’s conjecture was thatf(d)=d+1f(d) = d + 1. We prove thatf(d)≥(1.2)df(d) \geq (1.2)\sqrt dfor larged.
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